Hippogriff

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Each clue can have one letter doubled to yield a new word:

ClueAnswerNew WordDoubled Letter
Self-importance (3)EGOEGGOG
Hairdresser's workplace (5)SALONSALOONO
Russian money (5)RUBLERUBBLEB
Arduous, or IRS activity (6)TAXINGTAXIINGI
Long-barrelled gun (5)RIFLERIFFLEF
Suffocate, perhaps with a pillow (7)SMOTHERSMOOTHERO
Frightened (6)SCAREDSCARREDR
Cardboard milk container (6)CARTONCARTOONO
Bring to an end, like a job (6)FINISHFINNISHN
Part of a staircase (4)STEPSTEEPE

Reading the doubled letters gives GOBI FOR ONE, a clue for DESERT. Doubling a letter once again, the answer is therefore DESSERT.